The Fundamental frequency of an open organ pipe

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SUMMARY

The fundamental frequency of an open organ pipe is 261.6 Hz, corresponding to middle C. The third harmonic of a closed organ pipe matches this frequency, necessitating a comparison of their lengths. The correct formula for the frequency of an open pipe is given by frequency = n(v/2L), while for a closed pipe, it is frequency = (2n-1)(v/4L). Understanding these equations is crucial for solving problems related to the acoustics of organ pipes.

PREREQUISITES
  • Understanding of harmonic frequencies in acoustics
  • Familiarity with the speed of sound in air
  • Knowledge of basic physics equations related to wave motion
  • Concept of open and closed pipe resonances
NEXT STEPS
  • Study the derivation of harmonic frequencies for open and closed pipes
  • Learn about the speed of sound in different mediums
  • Explore the impact of pipe length on sound frequency
  • Investigate real-world applications of organ pipe acoustics
USEFUL FOR

Students studying physics, acoustics enthusiasts, and anyone interested in the principles of sound production in musical instruments.

jen0519
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Homework Statement



The fundamental frequency of an open organ pipe corresponds to the note middle C (f = 261.6 Hz on the chromatic musical scale). The third harmonic (f3) of another organ pipe that is closed at one end has the same frequency. Compare the lengths of these two pipes.


Homework Equations



frequency = harmonic number x (speed of sound in the pipe)/(2)(length of the vibrating air column)
frequency = harmonic number x (speed of sound in the pipe)/(4)(length of the vibrating air column)


The Attempt at a Solution



I'm not sure where to go from here
 
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Hi jen0519, welcome to PF.
Your relevant equation for open pipe is correct. But for closed pipe it is wrong.
It should be
Frequency = (2n + 1)(Speed of the sound)/4(length of the vibrating air column.)
 
It's normal to express this as
For the open pipe
Frequency= n(v/2L) where n=1,2,3,etc
For the closed pipe
Frequency=n(v/4L) where n=1,3,5, etc
or
Frequency=(2n-1) (v/4L) where n=1,2,3, etc
L is length of the pipe, v is speed of sound in the pipe
 

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